The paper presents a method for calculating the local and integral characteristics of the flow in the axisymmetric gas-dynamic paths of solid propellant rocket motors, taking into account the combustion of a charge of solid fuel. The numerical method of calculation is based on the use of the Godunov scheme, formulated for moving computational grids. The speed of movement of the combustion surface is defined locally on the edge of each calculation boundary cell. This approach allows us to take into account the uneven distribution of the pressure of the combustion products in the free volume of the combustion chamber. In test calculations, the power law of burning rate is used. Calculations of the gas flow in the solid propellant combustion chamber with cylindrical charge of solid fuel are carried out. Unsteady pressure curve in the combustion chamber is obtained. The method allows to determine all integral characteristics of the developed solid propellant rocket motors as a function of the engine running time.